Question

the difference between a two digit number and the number obtained by interchanging the digits is 36 what is the difference between the sum and the difference of the digits of the number it the ratio between the digiits of the number is 1:2

Answer 1

The ratio between the digits of the number is 1 : 2 
This information significantly LIMITS the possible values of the 2-digits. In fact, the number must be one of the following: 12, 24, 36 or 48 
So, rather that get all algebraic, the fastest approach is probably just testing the 4 possibilities to see which one satisfies the other information. 

We'll start with 12 
Reverse the digits to get 21 
21 - 12 = 9. No good. The difference is supposed to be 36 

How about 24? 
Reverse the digits to get 42 
42 - 24 = 18. No good. The difference is supposed to be 36 

How about 36? 
Reverse the digits to get 63 
63 - 36= 27. No good. The difference is supposed to be 36 

How about 48? 
Reverse the digits to get 84 
84 - 48= 36. BINGO!! 

What is the difference between the sum and the difference of the digits of the number? 
SUM of digits = 4 + 8 = 12 
DIFFERENCE of digits = 8 - 4 = 4 
So, the difference between the sum and the difference of the digits = 12 - 4 = 8 
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